Early Oct is a great time to go to HH. The weather is still very nice and the ocean pleasant. Temps will usually be in the 70's and evenings will begin to cool a little.
Don't miss a Dolphin cruise. There is also golf, tennis, canoeing, kayaking, shelling, crabbing, fishing and shopping. A tour of Savannah is always nice also. I'm sure you'll find plenty to do.